# The scores on a college entrance exam is 100 with a standard deviation of 7.5. How do you find the probability that a randomly selected score is between 85 and 100?

Jun 22, 2017

Proability that a randomly selected score is between $85$ and $100$ is 47.72%

#### Explanation:

Asumming that the distribution is normal, let us find the $z$ score of $85$ and $100$.

As $\mu = 100$ and $\sigma = 7.5$

$z$-score is given by $\frac{x - \mu}{\sigma}$

Hence for $85$, $z$-scorre is $\frac{85 - 100}{7.5} = - \frac{15}{7.5} = - 2$

and for $100$, $z$-scorre is $\frac{100 - 100}{7.5} = 0$

Hence area between $- 2$ and $0$ from tables is $0.4772$

and probability is 47.72%